An electric toothbrush is primarily a large rechargeable battery. In most cases it is nickel-cadmium. The other materials involved in the construction of an electric toothbrush are copper wire and small electric motor, with a plastic casing. Each one of these materials, in and of themselves, is certainly recyclable.
The question is whether or not people want to take the time to dismantle one in order to put it in a proper recycling bin.
The American Recycling Association estimates that it takes about 20 minutes to disassemble an electric toothbrush into its recyclable components. They recommend saving up discarded electric toothbrushes until you have enough to give to a Boy Scout troupe, who can then earn merit badges by taking them apart and taking the parts to a recycling center.